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Entropy 2012, 14(11), 2254-2264; doi:10.3390/e14112254

Statistical Information: A Bayesian Perspective

1,*  and 2
1 Department of Statistics, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA 2 Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-900, São Paulo, Brazil
* Author to whom correspondence should be addressed.
Received: 15 August 2012 / Revised: 28 September 2012 / Accepted: 1 November 2012 / Published: 7 November 2012
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We explore the meaning of information about quantities of interest. Our approach is divided in two scenarios: the analysis of observations and the planning of an experiment. First, we review the Sufficiency, Conditionality and Likelihood principles and how they relate to trivial experiments. Next, we review Blackwell Sufficiency and show that sampling without replacement is Blackwell Sufficient for sampling with replacement. Finally, we unify the two scenarios presenting an extension of the relationship between Blackwell Equivalence and the Likelihood Principle.
Keywords: statistical information; Blackwell sufficiency; likelihood principle statistical information; Blackwell sufficiency; likelihood principle
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Stern, R.B.; Pereira, C.A.B. Statistical Information: A Bayesian Perspective. Entropy 2012, 14, 2254-2264.

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